Bogus data assimilation

To better define the vortex structure in hurricane initial conditions, a bogus data assimilation (BDA) scheme is developed in the WRF-Var. The BDA algorithm includes: a) bogus vortex construction and error specification, and b) assimilation of the bogus data with the WRF-Var system. In our studies (Xiao et al., 2006; 2009b; Zhang et al., 2007), the bogus vortex is constructed according to the method of Ueno (1989; 1995). There are two components (symmetric and asymmetric) in the bogus observations. The asymmetric component comes from 3D-Var background (previous forecast).

The bogus vortex fields include SLP and wind profiles at various levels. The distribution of SLP within the bogus area is calculated by the following equation based on the Fujita (1952) formula,

where

In the equations of (14)-(16), r is the distance from the hurricane center (km), Ro is the radius of maximum wind, PC is the reported central SLP, and PB is the average SLP within RB. RB is a predefined radius of the bogus area.

The bogus symmetric wind is based on the gradient wind relation, f

Empirically, we include the effect of surface friction near the boundary layer by specifying smaller weightings. There are 7 levels (sea-level, 1000, 925, 850, 700, 600, 500 hPa) in the bogus wind profile. The weightings of the symmetric wind speed for each layer are 0.7, 0.8, 0.9, 1.0, 1.0, 1.0, 1.0, respectively. The divergence of upper air is difficult to determine. Therefore, the bogus symmetric winds are assigned 0 in the upper levels above 400 hPa. The asymmetric component is extracted from the WRF-Var background fields. When the background fields come from the WRF forecast, the position of the hurricane in the background fields can be different from observation. The asymmetric component is the difference between the background and the background typhoon symmetric component. Such asymmetric components are relocated to the right position and added to the symmetric bogus fields.

The bogus observation error is empirically specified. We assume that the error is linearly increased with respect to the distance from the typhoon center. Empirically, the specified errors of the bogus SLP and wind profiles are specified as follows:

rb where r is the distance from the hurricane center, z is the height, and RB is the calculated radius of the bogus area. The errors of the bogus SLP range from 1 hPa in the center to 4 hPa around the outmost edge of the bogus area, compared to the constant surface observation error (2 hPa) for SYNOP. Evo(z) represents the errors of the bogus wind at the center. Its values range from 1 m/s at the sea level to 3.3 m/s at 250 hPa, the same as the other wind errors (e.g. TEMP, SATOB, PILOT, etc.). The specified errors of the bogus wind at sea level range from 1 m/s in the center to 5 m/s around the outmost edge of the bogus area. The observation error specification is crucial in defining how the observation is used in a data assimilation system (Hollingsworth & Lonnberg, 1986). It determines how much of the observation is contributed to the analysis. However, the true values of the vortex bogus observation error are difficult to establish. The smaller error specified near the hurricane center implies more contribution from the bogus data near the center in the analysis. At the outmost edge of the bogus area, the bogus data have the smallest contribution. This also ensures a smooth transition of the analysis between the bogus area and the surrounding environment. In the BDA, the hurricane bogus fields are treated as supplemental observations and are assimilated during the WRF-Var analysis. The cost function in Eq. (1) includes the contributions of the bogus data in the observation term. The observational operators for the SLP and wind profiles in the WRF-Var system are just an interpolation scheme because SLP and winds are direct variable of the model.

To verify the capability of BDA, we selected twenty-one cases from seven hurricanes in the 2004 and 2005 seasons to conduct parallel experiments. They are Hurricanes Charley, Frances, Ivan, and Jeanne in 2004, and Katrina, Rita, and Wilma in 2005. We selected three cases for each hurricane before its landfall. These cases are very famous due to their striking effects to Florida in 2004 and devastating impacts in the Gulf of Mexico in 2005. Two parallel sets of experiments are carried out. The first set of experiments (CT) for all cases use GFS (Global Forecast System) analysis as background and assimilate only the conventional GTS. The second set of experiments (GB) is the same as CT but including BDA. The WRF 3D-Var experiments use the same background error covariance calculated from one-month statistics in September 2004 using the NMC method (Parish & Derber, 1992).

Figure 5 shows the mean absolute errors of the forecasts (position, CSLP, and MSW) against the best track observations at 24, 48, and 72 hours. The errors from the BDA experiments (GB) are smaller than that from control experiments (CT) for all of the verification parameters (position, CSLP, and MSW). Bogus data is able to remedy the data sparse issue in the vortex region and BDA improves the hurricane forecasting skill. We calculated the error reduction percentage by BDA from the statistics in Figure 5. The largest reduction of average error is in the forecast of CSLP, with 26.4% reduction of average error by BDA. The improvement in hurricane MSW is also significant; the average error is reduced by 24.0%. The track has the smallest but evident improvement among the three verification parameters.

Fig. 5. The mean absolute errors of the hurricane track (top), MSW (middle) and CSLP (bottom) for the forecasts from statistics of 21 cases in 2004 and 2005.

Due to model spin-up problem, both sets of experiments (CT and GB) present smaller CSLP and MSW errors at 48 and 72 hours than at 24 hour. However, the spin-up problem in GB is much less than in CT. BDA alleviates the spin-up problem, and produces larger hurricane intensity improvement at 24 hour than at 48 and 74 hours. The benefit of BDA in hurricane intensity forecasts becomes less with the increase of the forecast time (Fig. 5). The initial intensity using BDA in GB experiments is much closer to the observed than CT. With the model runs, the difference of intensity between GB and CT decreases, reflecting the model forecast at longer time is less sensitive to initial conditions than at shorter time. The improvement of hurricane CSLP and MSW in GB compared to CT at 24 hours is much more remarkable than that at 48 and 72 hours. In the track forecasts, however, experiment GB has the most significant improvement at 72 hours over the experiment CT.

Statistically, the improvement of hurricane intensity using BDA is more significant than that of hurricane track. It is further verified that the large-scale environment influences hurricane track, but that intensity is mainly impacted by hurricane's internal, dynamical and thermo-dynamical vortex structures. The BDA technique, which mainly improves the hurricane vortex structure according to the hurricane concept model, results in significant improvement of the hurricane intensity forecast. To support the assertion, we take Hurricane Katrina at 0000 UTC 26 August 2005 as an example to compare the vortex structures in CT and GB (Fig. 6). The CSLP and MSW errors are both reduced by BDA for Katrina initialized at 0000 UTC 26 August 2005. As shown in Figure 6, the hurricane positions of CT and GB are both very close to the observation. However, GB produces a vortex with lower CSLP and larger MSW than CT. BDA enhances the cyclone circulation and make the vortex much more compact. The area of the circular isobar with 1010hPa in GB is much reduced compared with that in CT. Note that the GFS analysis has its bogussing/relocation procedure, but it is apparently not sufficient for a good hurricane intensity forecast in the WRF ARW model. We verified that the initialization with BDA could improve the hurricane intensity forecast compared with the forecast from a simple GFS analysis.

Fig. 6. Hurricane Katrina at 0000 UTC 26 August 2005. The solid lines are SLP (with interval of 2.5 hPa and the barbs show 10-m wind field (a full barb represents 5 m/s) for (a) CT and (b) GB experiments.

The GFDL bogus scheme (Kurihara et a!., 1993) has been applied in hurricane initialization for over a decade. To further evaluate the performance of the BDA scheme in WRF 3D-Var, two parallel experiments on Hurricane Humberto at 1200 UTC 12 September 2007 are compared. The first experiment (CT) uses the WRF preprocessing system (WPS) to interpolate the GFDL analysis as initial conditions; and the second experiment (GB) uses the WRF 3D-Var procedure to initialize the hurricane vortex. The experiment GB uses GFS analysis as the first guess in WRF 3D-Var and assimilates the bogussing vortex plus conventional data. The forecasts for both experiments (CT and GB) are executed on 3 domains with the moving nested domains 2 and 3. The grid-spacings of the three domains are 12, 4, and 1.333 km, respectively.

10OW 90W SOW

Fig. 7. 72-h track forecast for Hurricane Humberto starting from 1200 UTC 12 to 1200 UTC 15 September 2007. Dashed line with "o" is the best track; the solid line with "*" is the forecast from CT experiment; and the grey line with "A" is the forecast from GB experiment. The date/hour are shown in boxes.

Figure 7 shows the forecasted tracks from experiments CT and GB as well as the best track for the period of 1200 UTC 12 - 1200 UTC 15 September 2007. The experiment CT, which has the vortex not well organized at the initial time, fails predicting the storm's inland movement. It lingers along the coastal area of Texas and Louisiana for two days, and then turns back to the Gulf of Mexico. Compared with the best track observation, CT fails to predict the storm's track. On the contrary, the experiment GB successfully predicts the storm's landfall and inland movement. Its predicted track follows the best track observation. Note that in Figure 7 the best track from the National Hurricane Center extends to 2100 UTC 14 September, while the prediction extends to 1200 UTC 15 September.

For the intensity prediction, CT also fails to predict the storm's intensification before landfall. Since it fails to predict the storms' intensification before landfall and fails to predict the storm's inland movement, its overall intensity forecast is not successful at all and therefore omitted in the comparison. In Figure 8, we thus only analyze the storm's intensity in GB and compare it with observation. The trends of CSLP (Fig. 8a) and MSW (Fig. 8b) from 1200 UTC 12 to 1200 UTC 15 September show good agreement between the forecast and observation. GB successfully predicts Humberto's intensification from a tropical storm (1200 UTC 12 September) to a Category-1 hurricane (0600 UTC 13 September) before its landfall over the Texas coast. The observation indicates the maximum intensity of Humberto at 0915 UTC 13 September with a CSLP of 986 hPa and a MSW of 85 kt (44 m/s). GB predicts the maximum intensity at 0945 UTC 13 September with a CSLP of 989 hPa and a MSW of 82 kt (43 m/s). However, it over-predicts Humberto's strength inland. At 0000 UTC 14 September, for example, GB predicts a CSLP of 997 hPa and a MSW of 37 kt (19 m/s), while the observations are 1006 hPa and 25 kt (13 m/s).

Fig. 8. 72-h intensity forecast for Hurricane Humberto starting from 1200 UTC 12 to 1200 UTC 15 September 2007: (a) Central sea level pressure (CSLP), and (b) Maximum surface wind (MSW). The solid line is the forecast from the GB experiment and dashed line is from the best track observation.

24h 36h 48 ti

Forecast Time (h)

Fig. 8. 72-h intensity forecast for Hurricane Humberto starting from 1200 UTC 12 to 1200 UTC 15 September 2007: (a) Central sea level pressure (CSLP), and (b) Maximum surface wind (MSW). The solid line is the forecast from the GB experiment and dashed line is from the best track observation.

5. Summary and conclusions

Hurricane initialization using the data in the vortex region is important for the intensity forecast. Doppler radar data and synthetic bogus data assimilations (BDA) have been implemented in WRF variational data assimilation (WRF-Var) system, and positive impacts on the analysis and forecast of hurricane structure and intensity have been obtained (Xiao et al., 2009a; b). The capability of airborne Doppler radar (ADR) data assimilation to improve hurricane initialization using WRF 3D-Var is examined for Hurricanes Jeanne (2004), Katrina (2005), and Rita (2005). The BDA technique is tested using 21 cases from 7 hurricanes in the 2004 and 2005 seasons. We also conducted one case study for Hurricane Humberto (2007), and compared the results between BDA and GFDL analyses for the WRF runs. The followings are highlights of our findings from the experiments:

• Assimilation of Doppler radial wind data markedly improve the representation of the hurricane vortex structure both at the initial time and in the forecast out to about 36 h. The ADR wind assimilation makes important contributions to improving hurricane intensity and structure forecasts. Hurricane track forecasts also benefited from assimilation of ADR wind data.

• The ADR reflectivity data assimilation in WRF 3D-Var system retrieves portion of the three-dimensional rainwater and cloud water fields of hurricane vortex at initialization. The multivariate responses in other variables are also reasonable. The addition of ADR data produces a realistic eye wall and associated strong convection. Rain bands are also favorably reorganized and appear more realistic.

• WRF hurricane forecasting using the BDA technique shows an improved forecast skill in hurricane track and intensity compared to initialization from just GFS analysis. Using the WRF 3D-Var system, the bogus SLP and wind profile data can be efficiently assimilated to recover the initial hurricane structure under 3D-Var statistical and physical balances. The forecasts of hurricane track and intensity are therefore improved.

• The enhancement of the hurricane forecast skill using BDA technique reflects in all forecast periods. With BDA, the largest improvement is in hurricane central pressure. The improvement in hurricane maximum surface wind is also statistically significant. The track has the smallest improvement among the three verification parameters.

• BDA with WRF 3D-Var performs well in a case study of Hurricane Humberto (2007), whereas WRF with the initial conditions interpolated from the GFDL analysis failed in the hurricane's landfall. More cases studies and real-time forecasts are necessary to further verify its performance. However, BDA with WRF 3D-Var for hurricane initialization has the potential to improve WRF hurricane forecasts.

One of the most challenges for the hurricane forecaster and researcher is to define the vortex structure in light of insufficient observations over the ocean. The Doppler radar data (from coastal radar or airborne Doppler radar) are valuable data source for hurricane structure. When there is no data at all in the vortex region, synthetic bogus data would help in defining the vortex structure. The BDA has shown promise in WRF hurricane forecasts. Usually, satellite data are less useful within the vortex due to cloud and rainfall contamination, limited spatial resolution, or suboptimal timing of observations (from polar orbiting platforms, for instance). Assimilating Doppler radar data or sometimes synthetic bogus vortex data is feasible and should be considered in forecasting of landfalling hurricanes so as to reduce the loss of life and property in coastal regions. In terms of WRF 3D-Var for hurricane vortex initialization, some limitations also exist. Firstly, a specific background error covariance for hurricanes should be developed and used in hurricane initialization. The background error statistics used in our studies are from the traditional NMC technique (Parrish & Derber, 1992). It is not totally suitable for the correlations in the hurricane vortex. The correlation of wind and pressure only presents large-scale feature. Secondly, reflectivity assimilation in WRF 3D-Var uses warm-rain process to bridge rainwater with other model variables in the analysis. At high levels above melting layer, however, ice-phase hydrometeors contribute to the most of reflectivity measurement. In this regard, a sophisticated microphysics that builds relationships among the whole hydrometeors and other dynamical and thermo-dynamical variables should be developed in WRF 3D-Var for radar reflectivity data assimilation. Finally, observation error statistics for radar observations and bogus data are only crudely represented at present. In addition, it should also be noted that most of our studies are based on the WRF 3D-Var that does not take into account the time differences but instead ingests data at one instant in time. 4D-Var should be a future direction for hurricane vortex initialization in order to better initialize the time dependence of the vortex necessary to accurately capture rapid intensity change as it is occurring.

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